My Dear President Obama,
Please go on TV and announce to the country that you are breaking off negotiations with the Republicans on this matter, having tried and found that there is not give-and-take and you feel they are playing with the country's well-being for low political purposes.
Announce that the U.S. does not and will not default on its debts. Announce that the debt ceiling is what the U.S. already spent or contracted for and it does not include any new debt that is outside of the promises that the U.S. has made.
If asked how. Tell them that you believe you have the legal authority to decree this. Let the Republicans scream their little Karl Rove lungs out.